Known photovoltaic (PV) cells, modules or arrays to use a maximum power point tracker (MPPT) to ensure that the maximum available power is extracted from the irradiated cells.
Known MPPT methods deliver a reference for the PV voltage, which is later used in a limited bandwidth proportional plus integral (PI) controller to generate the amplitude of the grid-side current reference.
FIG. 1 shows i-v and p-v curves of a PV panel in accordance with known systems. As shown in FIG. 1, the voltage and current output characteristic of a photovoltaic cell or module can be represented in the form of i-v or p-v curves. The i-v curve is the curve that starts at i=1 and ends at v=1, and the p-v curve is the curve having a maximum point when voltage v=VMPP.
Various electrical characteristics of PV panels are presented in FIG. 1. FIG. 1 shows the short circuit current (ISC), which is the maximum value of current cell can generate, and it is produced under short-circuit conditions (v=0 V). Open circuit voltage (VOC) corresponds to the highest value of voltage generated in open circuit conditions (i=0 A). Further, FIG. 1 shows the maximum power point (MPP), which is the operating point (voltage VMPP and current IMPP) where the PV cell produces the maximum power (PMPP=VMPP./IMPP).
The relationship between voltage and current can be expressed as the following implicit static nonlinearity
                    i        =                              I            SC                    ⁡                      [                          1              -                              exp                ⁡                                  (                                                            v                      -                                              V                        OC                                            +                                                                        R                          S                                                ·                        i                                                                                    V                      T                                                        )                                                      ]                                              (        1        )            
where VT is referred to as the thermal voltage, which is calculated according to the Boltzmann constant (K=1.38·10−23 J/K), magnitude of electron charge (q=1.6·10−19 C), PV temperature (T=(K)), idealizing factor (1<m<2) and number of cells in series (N), according to
            V      T        =          mNKT      q        ;RS is the series resistance, which depends on VMPP,IMPP,VOC and ISC under standard conditions and VT.
The previous expression (1) can be further reduced if RS<<1
                    i        =                              I            SC                    ⁡                      [                          1              -                              exp                ⁡                                  (                                                            v                      -                                              V                        OC                                                                                    V                      T                                                        )                                                      ]                                              (        2        )            
It should be noted that current i=i(v) is a static explicit nonlinear function of the voltage, i.e., dynamics are not considered. The power delivered by the PV module can be computed simply as a product of current and voltage as followsp=i·v  (3)
Manufacturers of photovoltaic cells and modules can provide the open circuit voltage (VOC), the short circuit current (ISC) and the maximum power point (PMPP=VMPP./IMPP) under standard test conditions (irradiance of 1000 W/m2 at 25° C. cell temperature). However, these parameters, and consequently the i-v PV characteristic, can be affected by temperature and solar irradiation as shown in FIG. 2.
FIG. 2 shows the influence of (a) solar irradiance and (b) cell's temperature on the PV i-v characteristic curve in accordance with known systems. FIG. 2 shows that the open circuit voltage VOC varies with both irradiance and temperature. VOC has a negative temperature coefficient and depends logarithmically on the irradiance. FIG. 2 also shows that, although the short circuit current ISC changes proportionally to the irradiance, it is relatively insensitive to temperature variation.
In any case, the MPP is varying in function of such environmental conditions, and thus it is important to have a strategy to guarantee the operation of the PV module on the MPP at all times. These strategies are referred to in known PV systems as maximum power point tracking (MPPT) algorithms.
The PV panel can be forced to operate in the MPP as shown in the p-v plot of FIG. 1. This operation guarantees that the power extracted from the PV module is the maximum power available. This objective can be recast as a regulation objective that can be fulfilled if one of the following is satisfied as t→∞:i→iMPP v→vMPP p→PMPP  (4)
where iMPP, vMPP and PMPP are the current, voltage and power in the MPP. In the context of the present disclosure, (·)* represents the reference for (·).
In the case of single-stage inverters, as those shown in FIGS. 3 and 4, this regulation objective is achieved by modulating the amplitude of the grid-side current i0. The reference for this current, referred to as P, can be generated by the MPPT algorithm. FIG. 3 shows a connection of the PV panel to the grid by means of a single-stage inverter, and controller using an indirect MPPT in accordance with known systems. FIG. 4 shows a connection of the PV panel to the grid by means of a known single-stage inverter in accordance with known systems.
FIGS. 3 and 4 illustrate a basic topology for the photovoltaic system. A solar panel, string or module 31 produces a DC voltage v. A capacitor C is connected in parallel with the panel, and the voltage from the parallel connection is fed to an inverter 32, which is presented in FIGS. 3 and 4 as a voltage source inverter (VSI). The output of the inverter is filtered with a filter 33 and fed further to the grid 34.
In known MPPT algorithms, the generation of P is performed indirectly by means of an intermediate PI controller 35 as shown in FIG. 3. As a result, the MPPT 36 generates the voltage reference vCref for the PV voltage vC, which is then compared to the measured vC, and the difference is used by the PI controller 35 to generate the amplitude P. The control block 40 includes a synchronization block 37, which reconstructs the frequency and phase of the grid voltage for producing a desired inverter output current, and a grid control block 38, which produces a voltage reference for the modulator 39. The PI controller should be tuned to have a relatively small bandwidth to alleviate the effect of the 2nd harmonic fluctuation. As a result, a poor dynamic response can be obtained as the response speed is considerably reduced.
The current reference can be computed from the obtained amplitude information P as
                              i          0          *                =                              P                          v                              S                ,                RMS                            2                                ⁢                      v                          S              ,              1                                                          (        5        )            
where vS,1 is the fundamental component of the grid voltage, and vS,RMS its RMS value. Usually vS,1 is obtained by means of an external PLL or any other synchronization process. A current control loop can be designed to guarantee that the grid-side current i0 follows such a reference i0* defined above in an accurate and fast manner.
FIG. 5 shows a connection of the PV panel to the grid by means of a known dual-stage inverter in accordance with known systems. In the case of dual-stage converters, as shown in FIG. 5, the MPPT generates the voltage reference vref for the input capacitor CPV (PV voltage), which is then used to compute the duty ratio u in block 54 for the DC-DC converter 51. In dual-stage topologies, the output voltage of the DC-DC converter can be controlled by the inverter, while the input voltage v is controlled by the DC-DC converter. That is, the DC-DC converter 51 is responsible for guaranteeing the operation in the MPP. The amplitude P for the current reference can be generated by a PI controller 52 that guarantees the regulation of the capacitor voltage vC. towards a given constant reference vCref. The voltage reference vCref is a design parameter defined externally. The amplitude P is fed to a grid control block 55, which operates to produce a voltage reference e for producing a desired current i1.
The most common MPPT algorithms are the constant voltage (CV), the perturbation and observation (P&O) and the incremental conductance (IncCond), and modifications to them. In known systems, both P&O and IncCond are based on a perturb and observe approach. This approach comprises perturbing the PV voltage by adding or subtracting a small step and then observing the resulting changes in power. A decision based on these changes is made to decrease or increase the PV voltage in the next sampling time.
From these algorithms, a reference for the PV voltage can be obtained, which is used in a PI system to generate the final control signal, such as the amplitude of the reference for the grid-side current. Both methods, P&O and IncCond, usually oscillate close to the MPP as they are based on a perturb and observe process. On the other hand, the CV has no oscillations but it rarely reaches the MPP.
In known MPPT systems, performance suffers from fluctuations under rapidly changing atmospheric conditions. It has been observed that P&O suffers from big excursions (e.g., fluctuations) in the wrong direction after rapidly changing irradiation conditions, that is, P&O fails to track the MPP effectively, while IncGond may still show good accuracy and efficiency in these conditions.
Other known MPPT methods comprise reconstructing the variation of power with respect to voltage on the PV (dp/dv) or the variation of power with respect to the duty ratio of the DC-DC converter attached to the PV (dp/dD) is used. These methods address the problem of attaching a battery charger after the DC-DC converter, which restricts the output voltage to be constant. Thus, the maximization of output power turns out to be equivalent to maximizing the output current of the DC-DC converter. Hence, the measurement of the PV voltage becomes unnecessary. Based on the known MPPT methods the PV power is no longer maximized but rather the power after the DC-DC converter is maximized, which is referred as the actual usable power.
A common drawback in known MPPT schemes concerns specifying that current be measured from the PV panel.